This past Friday brought news that the U.S. economy added 157,000 jobs in July, dropping unemployment to 3.9 percent. The unemployment rate has only gotten that low twice before in the last 50 years.

Yet this spectacular performance has come with two bitter mysteries: Wage growth remains sluggish and productivity growth is pathetic.

Economists aren't sure what to make of these twin puzzles: Some think there are two separate explanations; others that the productivity slowdown explains wages.

But maybe the simplest explanation is that the two mysteries are one and the same.

Jason Furman, who headed up the White House Council of Economic Advisers for four years under former President Barack Obama, recently made the case that productivity explains wages. His main proof is a fairly detailed statistical analysis of the labor markets, which he finds are as tight today as they were during the economic boom of the late 1990s. When employers have that much trouble finding workers, the former usually have to boost their offers to attract the latter. Presto: Wage growth. But since wages aren't rising rapidly, that leaves two suspects: productivity growth is too low or inequality is rising.

Furman dismisses the inequality argument quickly because inequality is, well, not rising. It's high, but it has plateaued.

That leaves productivity growth, a known ingredient of wage growth. Basically, the faster companies figure out how to produce more value with less inputs, the more money they have to pass on to employees. If productivity growth is low, that could explain why wages aren't growing as quickly as they should be.

But Josh Bivens of the Economic Policy Institute noted that productivity growth isn't the only thing that's low compared to the late '90s. The rate of price growth is also low, which suggests too much labor market slack. The collapse of employer investment in worker training and the spread of absurd employer demands for college degrees in all sorts of occupations also both point to a labor market in which employers can still afford to be picky. The unemployment rate may be the same as it was in the '90s, but labor force participation remains lower. Furman's own CEA concluded the drop couldn't be chalked up purely to demographics, and was partly driven by the poor post-2008 economy. It's hard to square all this evidence with the idea that labor markets really are as tight now as they were in the late '90s.

More to the point, though, maybe we shouldn't think of labor market tightness and productivity growth as two entirely separate factors feeding into wage growth.

Companies don't just adopt better technologies or business models because they can. They do so because they feel they must. And they feel that need most acutely when the workers they need to expand are scarce and expensive. A good historical example is retail: Technologies like barcodes, electronic monitoring of shelf levels, digital finance tools, and more were all available in the 1980s or even the 1970s. But they weren't actually put to widespread use in the industry until the late '90s — probably because that was when companies ran out of cheap labor and had to start getting creative to compete. Previous periods of high productivity growth — in the midcentury, late '90s, and early 2000s — similarly coincided with periods when we know for sure labor markets were really tight.

Now, Bivens and Furman's differences don't necessarily translate to the practical policy level. They both seem to think the Fed should lay off interest rate hikes and let the economy run hotter. They think we need stronger unions and a higher minimum wage and more public investment.

But it's worth noting we don't need to complicate the message about wages by trying to strictly separate out productivity from labor market tightness. Most likely these are a single interlocking story.